Problem: $h(t) = -2t^{2}+4(g(t))$ $g(t) = -6t$ $ g(h(-6)) = {?} $
Explanation: First, let's solve for the value of the inner function, $h(-6)$ . Then we'll know what to plug into the outer function. $h(-6) = -2(-6)^{2}+4(g(-6))$ To solve for the value of $h$ , we need to solve for the value of $g(-6)$ $g(-6) = (-6)(-6)$ $g(-6) = 36$ That means $h(-6) = -2(-6)^{2}+(4)(36)$ $h(-6) = 72$ Now we know that $h(-6) = 72$ . Let's solve for $g(h(-6))$ , which is $g(72)$ $g(72) = (-6)(72)$ $g(72) = -432$